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Dynamic Net of a Square-Based Pyramid for Surface Area Exploration

Dynamic Net of a Square-Based Pyramid for Surface Area Exploration
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2014-01-12 02:23
PolygonSolid GeometryGeometric ConstructionSlider Animation
This GeoGebra example presents a dynamic open-out (net) of a square-based pyramid, allowing users to visually unfold the 3D solid into its 2D faces. It is designed to discuss basic properties of the pyramid and compute its total surface area. Core mathematical concepts include the base square, lateral triangular faces, the relationship between the net and the solid, and the formula for total surface area. Construction highlights: using GeoGebra commands such as Circle, Point, Segment, Polygon, Midpoint, OrthogonalLine, Intersect, PointIn, and Distance to build the base, apex, and auxiliary lines; sliders and dynamic polygons (çokgen1–çokgen4) represent the unfolding faces. Suitable for middle school to high school students learning solid geometry, surface area calculations, or interactive geometric demonstrations.

GeoGebra Commands & Parameters

  1. Circle(A, a) → c
  2. Point(c) → B
  3. Segment(A, B) → b
  4. Polygon(A, B, 4) → çokgen1, d, e_1, f_1, g_1, C, D
  5. Midpoint(D, C) → E
  6. Circle(E, h) → f
  7. OrthogonalLine(E, f_1) → g
  8. Intersect(f, g) → F, G
  9. Segment(E, F) → h_2
  10. Segment(D, F) → i
  11. Segment(C, F) → j
  12. Circle(F, h) → k
  13. Circle(F, D) → p
  14. Circle(D, a) → q
  15. Intersect(q, p) → H, I, ,
  16. Polygon(H, F, D) → çokgen2, d_1, h_1, f_2
  17. Polygon(D, F, C) → çokgen3, c_1, d_2, f_3
  18. Circle(C, a) → r
  19. Intersect(p, r) → K, K_1, ,
  20. Polygon(F, K, C) → çokgen4, c_2, f_4, k_1
  21. Circle(K, a) → s
  22. Intersect(p, s) → L, L_1, ,
  23. Polygon(F, K, L) → çokgen5, l, f_5, k_2
  24. PointIn(çokgen1) → Noktaçokgen1
  25. PointIn(çokgen2) → Noktaçokgen2_1
  26. PointIn(çokgen3) → Noktaçokgen3
  27. PointIn(çokgen4) → Noktaçokgen4
  28. PointIn(çokgen5) → Noktaçokgen5
  29. Distance(H, F) → HF
  30. PointIn(çokgen2) → Noktaçokgen2

AI Drawing Prompt Reference

Draw an unfoldable net of a square-based pyramid with a square base and four triangular lateral faces, where the base size is adjustable via a slider. The four triangular faces dynamically unfold around the square base, showing the pyramid's net structure, with key points, auxiliary lines, and labeled triangular faces for surface area calculation.
The prompt above was compiled from the original drawing commands and is for reference only.